# Numbers Divisible by 9

Table below shows a list of multiples of 9 and the sum of their digits. We realised that, the sum of the digits is also multiple of 9.

 Multiples of 9 Sum of the digits 9 9 18 1 + 8 = 9 27 2 + 7 = 9 36 3 + 6 = 9 45 4 + 5 = 9 54 5 + 4 = 9 63 6 + 3 = 9 72 7 + 2 = 9 81 8 + 1 = 9 90 9 + 0 = 9 99 9 + 9 = 18 1 + 8 = 9 108 1 + 0 + 8 = 9 117 1 + 1 + 7 = 9 126 1 + 2 + 6 = 9 135 1 + 3 + 5 = 9 144 1 + 4 + 4 = 9 153 1 + 5 + 3 = 9 162 1 + 6 + 2 = 9 171 1 + 7 + 1 = 9 180 1 + 8 + 0 = 9 189 1 + 8 + 9 = 18 1 + 8 = 9 198 1 + 9 + 8 = 18 1 + 8 = 9 207 2 + 0 + 7 = 9 216 2 + 1 + 6 = 9 225 2 + 2 + 5 = 9 234 2 + 3 + 4 = 9 243 2 + 4 + 3 = 9 252 2 + 5 + 2 = 9 261 2 + 6 + 1 = 9

Therefore, we can conclude that
If the sum of the digits of a number is divisible by 9, the number must also divisible by 9
or
If the sum of the digits of a number is a multiple of 9, the number must also a multiple of 9.
For example:
Is 972635 a multiple of 9?

Sum of the digits:
9 + 7 + 2 + 6 + 3 + 5 = 32

32 is not multiple of 9, hence 972635 is not a multiple of 9.

Let's see another example:
Is 683746533 divisible by 9?

Sum of the digits:
6 + 8 + 3 + 7 + 4 + 6 + 5 + 3 + 3 = 45

45 is divisible by 9, hence 683746533 is divisible by 9